Simplify the following expression: $r = \dfrac{t^2 + 14t + 48}{t + 6} $
Answer: First factor the polynomial in the numerator. $ t^2 + 14t + 48 = (t + 6)(t + 8) $ So we can rewrite the expression as: $r = \dfrac{(t + 6)(t + 8)}{t + 6} $ We can divide the numerator and denominator by $(t + 6)$ on condition that $t \neq -6$ Therefore $r = t + 8; t \neq -6$